PSI - Issue 38

L. Heindel et al. / Procedia Structural Integrity 38 (2022) 159–167 L. Heindel t al. / Structural Integrity Procedia 00 (2021) 00 –000

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Fig. 1: A continuous prediction (bottom) is generated by using a weighting function (middle) to interpolate between subsequence predictions (top).

by the standard deviation in each measurement channel to ensure a new mean of zero and a standard deviation of one across the training dataset. This preprocessing step improves the training process and is later reverted for each prediction the network generates. The LSTM is now trained to accurately predict output subsequences from given input subsequences. Afterwards, the individual predictions are recombined using a weighting scheme, depicted in Figure 1 for a single signal channel. The chosen Welch window function, raised to the power of 10, interpolates between overlapping predictions and ensures that the beginning and end of each subsequence do not influence the combined prediction. To still generate a valid prediction at the beginning of the measurement data, an additional subsequence is introduced, which spans the timesteps from − L / 2 to L / 2. Its unmeasured input channel values are each set to equal the first available data points. An FRF model perfectly predicts linear relationships between the input and output channels of a time-invariant dynamic system and can be parameterized with comparatively low computational e ff ort and data requirements. In contrast, the LSTM network requires a computationally intensive training process using a large dataset, but is able to predict highly non-linear system behavior much more accurately. A hybrid model aims to combine both approaches in order to profit from the good baseline estimate of the FRF model, which is enhanced by the LSTM network to enable predictions of non-linear relationships. This paper o ff ers two di ff erent strategies to hybrid model creation. In the first approach, denoted by hybrid 1 , the FRF model creates a prediction, which is then subtracted from the true system response. The remaining model error is then used as the training output data of an LSTM network, which receives the same input data as the FRF model. The LSTM network then learns to approximate the modeling error of the FRF model and can simply be added to the previous prediction as a correcting term. In the second approach, denoted by hybrid 2 , the FRF prediction is instead added to the input data of the LSTM network. As a result, the network already contains a baseline solution to the 2.3. Hybrid modeling strategies